Quasi-synchronization of heterogeneous stochastic coupled reaction-diffusion neural networks with mixed time-varying delays via boundary control

•Firstly, compared with the homogeneous system, the more general heterogeneous coupled neural network model is studied here. By processing the heterogeneous terms, the mean-square quasi-synchronization problem under the influence of stochastic disturbance is solved.•Secondly, on the basis of discussing the influence of communication time-delay, this paper also considers various time-delays such as distributed time-delay, transmission time-delay. According to the existing conclusions of time-delay systems, we extend it to heterogeneous CNNs, and obtain a sufficient condition for time-invariant delay.•Finally, in the reaction-diffusion environment, compared with the conventional controller, a more advantageous boundary controller is designed. At the same time, the corresponding boundary control under mixed boundary conditions is proposed, and the final system is uniformly ultimately bounded.